Exercise n. 2 Consider a duopolistic market characterized by the inverse demand function P(() = A - Q. The cost function of each firm is given by C(q ) = cq, (1 = 1,2). The two firms are located in different countries and sell their goods in a third country. Assume that country /'s government decides to give a subsidy s per unit of output to the domestic firm. The game develops in two stages: in the first stage of the game the government of country / chooses the level of the subsidy s; in the second stage the two firms choose the output levels, q, and 92. The objective function of the government of country / is Gl = - sq1- 2.a) Suppose that the two firms compete a' la Cournot. Determine the quantities produced by the two firms. government of country / is G! = [' - sq1 . Suppose now that firm 2 is characterized by separation between management and ownership, like in the models by Sklivas and Fershtman and Judd. In the first stage of the game the government of country / chooses the subsidy s (as in the previous point), whereas the owners of firm 2. who want to maximize firm 2's profits, choose the weight a to be given to profits in the manager's compensation. In the second stage firm / chooses q, to maximize profits and the manager of firm 2 chooses q2 so as to maximize his compensation, i.e. a weighted average of profits and revenues, with weights respectively given by a and (1 - a). 2.b) Derive the level of output produced by each firm (q, and 92) as a function of s and a. 2.c) Derive the equilibrium values of s and a and show that equilibrium quantities are the same as in the Fershtman and Judd's model